Question

This question combines geometry and algebra. Refer to the geometrical construction, find the unknown values?

Answer 1

`x = 10`

Explanation:

There is a theorem that states

`bar(DE)cdot bar(EC) = bar(AE) cdot bar(EB)`

(Additional information at https://en.wikipedia.org/wiki/Power_of_a_point)

so

`4x=1/2x(x-2)`

Solving for `x` we obtain

`x = 0` which is unfeasible and `x = 10` which is feasible